Search Results (13)

Entropic soft-min operators are widely used to obtain smooth approximations of minimum and argmin mechanisms in optimization, machine learning, and reinforcement learning. The quality of this approximation is controlled by an inverse temperature parameter that governs the trade-off between smoothness and fidelity, yet its selection is usually based on global heuristics or worst-case bounds that do not account for the geometry of the candidate cost vector. This study investigates the calibration of the inverse temperature parameter from a geometry-aware perspective, with explicit guarantees on the approximation error between the entropic soft-min and the exact minimum value. After establishing the structural properties of the relaxation error, including monotonicity with respect to the inverse temperature and its dependence on the geometry of the near-optimal set, we introduce a conformal calibration rule that selects the smallest inverse temperature, ensuring that a prescribed upper quantile of the approximation error remains below a target tolerance with distribution-free finite-sample validity. The resulting selector adapts to the geometry distribution represented in the calibration population and provides a principled alternative to mean-based and worst-case tuning rules. Numerical experiments, including geometry-controlled benchmarks and a contextual bandit setting illustrating the impact of geometry-aware calibration on decision-making under estimated action values, show that the proposed method accurately tracks oracle calibration temperatures, preserves the desired operator-level coverage, and makes explicit how geometric heterogeneity governs the effective sharpness required by the soft-min approximation. Additional shifted evaluations illustrate the role of exchangeability in the validity guarantee and the consequences of transferring temperatures across populations with different near-optimal geometries. Full article

Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its principled selection is typically heuristic. This work studies the data-driven calibration of the inverse temperature parameter governing the entropic soft-min relaxation, with explicit guarantees on the relaxation error between the soft-min operator and the infimum of the cost function. After establishing monotonicity properties and approximation bounds for the relaxation error, we introduce a conformal calibration rule that selects the smallest inverse temperature ensuring that the approximation error satisfies a prescribed tolerance with distribution-free finite-sample validity. The resulting selector adapts to the distribution of candidate cost-vector geometries represented in the calibration sample, enabling regime-specific inverse temperature selection in heterogeneous settings. Numerical experiments, including an adaptive cruise control application with safety filtering, show that the proposed method accurately tracks oracle calibration inverse temperatures and achieves near-target coverage in the exchangeable setting covered by the theory, while an additional shifted evaluation illustrates the role of this assumption. Full article

Accurately forecasting the operating temperature of lithium-ion batteries (LIBs) is essential for preventing thermal runaway, extending service life, and ensuring the safe operation of electric vehicles and stationary energy-storage systems. This work introduces a unified, physics-informed, and data-driven temperature-prediction framework that integrates mathematically governed preprocessing, electrothermal decomposition, and sequential deep learning architectures. The methodology systematically applies the governing relations to convert raw temperature measurements into trend, seasonal, and residual components, thereby isolating long-term thermal accumulation, reversible entropy-driven oscillations, and irreversible resistive heating. These physically interpretable signatures serve as structured inputs to machine learning and deep learning models trained on temporally segmented temperature sequences. Among all evaluated predictors, the Bidirectional Long Short-Term Memory (BiLSTM) network achieved the highest prediction fidelity, yielding an RMSE of 0.018 °C, a 35.7% improvement over the conventional Long Short-Term Memory (LSTM) (RMSE = 0.028 °C) due to its ability to simultaneously encode forward and backward temporal dependencies inherent in cyclic electrochemical operation. While CatBoost exhibited the strongest performance among classical regressors (RMSE = 0.022 °C), outperforming Random Forest, Gradient Boosting, Support Vector Regression, XGBoost, and LightGBM, it remained inferior to BiLSTM because it lacks the capacity to represent bidirectional electrothermal dynamics. This performance hierarchy confirms that LIB thermal evolution is not dictated solely by historical load sequences; it also depends on forthcoming cycling patterns and entropic interactions, which unidirectional and memoryless models cannot capture. The resulting hybrid physics-data-driven framework provides a reliable surrogate for real-time LIB thermal estimation and can be directly embedded within BMS to enable proactive intervention strategies such as predictive cooling activation, current derating, and early detection of hazardous thermal conditions. By coupling physics-based decomposition with deep sequential learning, this study establishes a validated foundation for next-generation LIB thermal-management platforms and identifies a clear trajectory for future work extending the methodology to module- and pack-level systems suitable for industrial deployment. Full article

Entropy-based image thresholding is one of the most widely used segmentation techniques in image processing. The Tsallis and Masi entropies are information measures that can capture long-range interactions in various physical systems. On the other hand, Shannon entropy is more appropriate for short-range correlations. In this paper, we have improved a thresholding technique based on Tsallis and Shannon formulas by using Masi entropy. Specifically, we replace the Tsallis information measure with Masi’s one, obtaining better results than the original methodology. As the proposed method depends on an entropic parameter, we designed a thresholding algorithm that incorporates a simulated annealing procedure for parameter optimization. Then, we compared our results with thresholding methods that use just Masi (or Tsallis), or a combination of them, Shannon, Sine, and Hill entropies. The comparison is enriched with a kernel version of a support vector machine, as well as a discussion of our proposal in relation to deep learning approaches. Quantitative measures of segmentation accuracy demonstrated the superior performance of our method in infrared, nondestructive testing (NDT), as well as RGB images from the BSDS500 dataset. Full article

Homeostasis, which supports and maintains brain function, results from the continuous regulation of thermodynamics within tissue: the balance of heat production, redox oscillations, and vascular convection regulates coherent energy flow within the organ. Neuroinflammation disturbs this balance, creating measurable entropy gradients that precede structural damage to its tissue components. This paper proposes that a thermodynamic unity can be devised that incorporates nanoscale physics, energetic neurophysiology, and systems neuroscience, and can be used to understand and treat neuroinflammatory processes. Using multifactorial modalities such as quantum thermometry, nanoscale calorimetry, and redox oscillometry we define how local entropy production (s_t), relaxation time (τ^R), and coherence lengths (λc) allow quantification of the progressive loss of energetic symmetry within neural tissues. It is these variables that provide the basis for the etiology of thermodynamic biomarkers which on a molecular-redox-to-network scale characterize the transitions governing the onset of the neuroinflammatory process as well as the recovery potential of the organism. The entropic probing of systems (PEP) further allows the translation of these parameters into dynamic patient-specific trajectories that model the behavior of individuals by predicting recurrent bouts of instability through the application of machine learning algorithms to the vectors of entropy flux. The parallel development of the nanothermodynamic intervention, which includes thermoplasmonic heat rebalancing, catalytic redox nanoreacting systems, and adaptive field-oscillation synchronicity, shows by example how the corrections that can be applied to the entropy balance of the cell and system as a whole offer a feasible form of restoration of energy coherence. Such closed loop therapy would not function by the suppression of inflammatory signaling, but rather by the re-establishment of reversible energy relations between mitochondrial, glial, and vascular territories. The combination of these factors allows for correction of neuroinflammation, which can now be viewed from a fresh perspective as a dynamic phase disorder that is diagnosable, predictable, and curable through the physics of coherence rather than the molecular suppression of inflammatory signaling. The significance of this set of ideas is considerable as it introduces a feasible and verifiable structure to what must ultimately become the basis of a new branch of science: predictive energetic medicine. It is anticipated that entropy, as a measurable and modifiable variable in therapeutic “inscription”, will be found to be one of the most significant parameters determining the neurorestoration potential in future medical science. Full article

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed. Full article

The increasingly pervasive problem of counterfeiting affects both individuals and industry. In particular, public health and medical fields face threats to device authenticity and patient privacy, especially in the post-pandemic era. Physical unclonable functions (PUFs) present a modern solution using counterfeit-proof security labels to securely authenticate and identify physical objects. PUFs harness innately entropic information generators to create a unique fingerprint for an authentication protocol. This paper proposes a facile protein self-assembly process as an entropy generator for a unique biological PUF. The posited image digitization process applies a deep learning model to extract a feature vector from the self-assembly image. This is then binarized and debiased to produce a cryptographic key. The NIST SP 800-22 Statistical Test Suite was used to evaluate the randomness of the generated keys, which proved sufficiently stochastic. To facilitate deployment on physical objects, the PUF images were printed on flexible silk-fibroin-based biodegradable labels using functional protein bioinks. Images from the labels were captured using a cellphone camera and referenced against the source image for error rate comparison. The deep-learning-based biological PUF has potential as a low-cost, scalable, highly randomized strategy for anti-counterfeiting technology. Full article

Kernel methods have played a major role in the last two decades in the modeling and visualization of complex problems in data science. The choice of kernel function remains an open research area and the reasons why some kernels perform better than others are not yet understood. Moreover, the high computational costs of kernel-based methods make it extremely inefficient to use standard model selection methods, such as cross-validation, creating a need for careful kernel design and parameter choice. These reasons justify the prior analyses of kernel matrices, i.e., mathematical objects generated by the kernel functions. This paper explores these topics from an entropic standpoint for the case of kernelized relevance vector machines (RVMs), pinpointing desirable properties of kernel matrices that increase the likelihood of obtaining good model performances in terms of generalization power, as well as relate these properties to the model’s fitting ability. We also derive a heuristic for achieving close-to-optimal modeling results while keeping the computational costs low, thus providing a recipe for efficient analysis when processing resources are limited. Full article

Costa et. al (Frontiers in Physiology (2017) 8255) proved that abnormal features of heart rate variability (HRV) can be discerned by the presence of particular patterns in a signal of time intervals between subsequent heart contractions, called RR intervals. In the following, the statistics of these patterns, quantified using entropic tools, are explored in order to uncover the specifics of the dynamics of heart contraction based on RR intervals. The 33 measures of HRV (standard and new ones) were estimated from four hour nocturnal recordings obtained from 181 healthy people of different ages and analyzed with the machine learning methods. The validation of the methods was based on the results obtained from shuffled data. The exploratory factor analysis provided five factors driving the HRV. We hypothesize that these factors could be related to the commonly assumed physiological sources of HRV: (i) activity of the vagal nervous system; (ii) dynamical balance in the autonomic nervous system; (iii) sympathetic activity; (iv) homeostatic stability; and (v) humoral effects. In particular, the indices describing patterns: their total volume, as well as their distribution, showed important aspects of the organization of the ANS control: the presence or absence of a strong correlation between the patterns’ indices, which distinguished the original rhythms of people from their shuffled representatives. Supposing that the dynamic organization of RR intervals is age dependent, classification with the support vector machines was performed. The classification results proved to be strongly dependent on the parameters of the methods used, therefore determining that the age group was not obvious. Full article

Heisenberg’s uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in various ways. The relative entropy is the natural theoretical quantifier of the information loss when a `true’ probability distribution is replaced by an approximating one. In this paper, we provide a lower bound for the amount of information that is lost by replacing the distributions of the sharp position and momentum observables, as they could be obtained with two separate experiments, by the marginals of any smeared joint measurement. The bound is obtained by introducing an entropic error function, and optimizing it over a suitable class of covariant approximate joint measurements. We fully exploit two cases of target observables: (1) n-dimensional position and momentum vectors; (2) two components of position and momentum along different directions. In (1), we connect the quantum bound to the dimension n; in (2), going from parallel to orthogonal directions, we show the transition from highly incompatible observables to compatible ones. For simplicity, we develop the theory only for Gaussian states and measurements. Full article

Surface tension and surface energy are closely related, although not identical concepts. Surface tension is a generalized force; unlike a conventional mechanical force, it is not applied to any particular body or point. Using this notion, we suggest a simple geometric interpretation of the Young, Wenzel, Cassie, Antonoff and Girifalco–Good equations for the equilibrium during wetting. This approach extends the traditional concept of Neumann’s triangle. Substances are presented as points, while tensions are vectors connecting the points, and the equations and inequalities of wetting equilibrium obtain simple geometric meaning with the surface roughness effect interpreted as stretching of corresponding vectors; surface heterogeneity is their linear combination, and contact angle hysteresis is rotation. We discuss energy dissipation mechanisms during wetting due to contact angle hysteresis, the superhydrophobicity and the possible entropic nature of the surface tension. Full article

A computational procedure is developed to determine initial instabilities within a three-dimensional laminar boundary layer and to follow these instabilities in the streamwise direction through to the resulting intermittency exponents within a fully developed turbulent flow. The fluctuating velocity wave vector component equations are arranged into a Lorenz-type system of equations. The nonlinear time series solution of these equations at the fifth station downstream of the initial instabilities indicates a sequential outward burst process, while the results for the eleventh station predict a strong sequential inward sweep process. The results for the thirteenth station indicate a return to the original instability autogeneration process. The nonlinear time series solutions indicate regions of order and disorder within the solutions. Empirical entropies are defined from decomposition modes obtained from singular value decomposition techniques applied to the nonlinear time series solutions. Empirical entropic indices are obtained from the empirical entropies for two streamwise stations. The intermittency exponents are then obtained from the entropic indices for these streamwise stations that indicate the burst and autogeneration processes. Full article

The gravity and magnetic data measured on the Earth’s surface or above it (collected from an aircraft flying at low altitude) can be used to assist in geologic mapping by estimating the spatial density and magnetization distributions, respectively, presumably confined to the interior of a horizontal slab with known depths to the top and bottom. To estimate density or magnetization distributions we assume a piecewise constant function defined on a user-specified grid of cells and invert the gravity or magnetic data by using the entropic regularization as a stabilizing function that allows estimating abrupt changes in the physical-property distribution. The entropic regularization combines the minimization of the first-order entropy measure with the maximization of the zeroth-order entropy measure of the solution vector. The aim of this approach is to detect sharp-bounded geologic units through the discontinuities in the estimated density or magnetization distributions. Tests conducted with synthetic data show that the entropic regularization can delineate discontinuous geologic units, allowing a better mapping of sharp-bounded (but buried) geologic bodies. We demonstrate the potential of the entropic regularization to assist a geologist in obtaining a geologic map by analyzing the estimated magnetization distributions from field magnetic data over a magnetic skarn in Butte Valley, Nevada, U.S.A. We show that it is an exoskarn where the ion exchange between the intrusive and the host rock occurs along a limited portion of the southern intrusive border. Full article